Beneficial and Harmful Mutations

"these estimates of the proportions of deleterious and beneficial mutations have to be considered as lower bounds, because some of the mutations classified as neutrals could actually have a fitness effect too weak to be detected by our experimental method" — Rafael Sanjuán and colleagues, 2004¹

Summary

There is no single answer to "what share of new mutations is harmful or helpful."  Every published figure depends on four things:  what was counted (a random point mutation, an engineered amino-acid change, a transposon insertion, a whole mutation-accumulation line, or a class in a fitted model), what was measured (growth in a flask, drug resistance, fluorescence, egg-to-adult survival, or a population-genetic fit), the conditions of the test, and the smallest effect the method could see.  The reference tables in Part 1 keep those apart.  Read across them, the evidence supports seven findings.

1. Lethal mutations are common in compact genomes. Of random single-letter changes made one at a time in small viruses, 20% to 41% killed the virus (Part 2). A yeast screen built to find harmful mutations found 20 lethal among the 69 spontaneous mutations it picked up; that share describes the class the screen was designed to catch, not all new mutations. Neither figure is a share for large genomes with much non-coding DNA, which this article does not try to estimate.
2. Among mutations with a measurable effect, harmful ones outnumber helpful ones in most of the sets reviewed here. In the two random virus sets that tested every mutant for significance and found any beneficial one, harmful plus lethal mutants outnumber beneficial ones by 16.5 to 1 (vesicular stomatitis virus) and 22.5 to 1 (phage f1). A third virus set and a set of random E. coli insertions found no significantly beneficial mutant. Most gene-wide scans lean the same way, though 3 of the 22 compared by Reeb and colleagues found more beneficial than harmful changes. The mainstream review of the subject says plainly that "advantageous mutations are rare."² That is also what standard population genetics expects of an organism near an adaptive peak, so the predominance of harmful mutations does not by itself tell a young earth from an old one.
3. "Rare" in these sets means a few percent, not one in a million, and the share changes with organism, design and conditions. In the three virus sets tested for significance, beneficial mutants were 0% to about 6% of the mutants with a detectable effect and 0% to about 4% of all tested (Part 2). Other designs give more. Fits to yeast mutation-accumulation lines put 5.75% to 13% of fitness-altering mutations on the beneficial side, with wide intervals and the authors' own reasons the figures may be too high;³ an alga gave about one-sixth of mutations with effects over 1%; and 3 of 22 gene scans found a beneficial majority under their own readouts (Parts 2 and 3). No one of these is a share for all life.
4. "Neutral" in a laboratory table means "not told apart from zero by this assay." Most assays reviewed here resolve effects of about 0.1% to 5%. The finest single-mutation precision quoted among them is about 0.02%, for the mean selection coefficients of three E. coli mutants.⁴ The authors of the viral studies treat their neutral classes as upper bounds and their harmful and beneficial classes as lower bounds, which holds to the extent that their significant calls are right. Human population-genetic fits reach smaller effects, but only for whole classes, through a fitted population history, and usually with no beneficial class unless one is added (Part 5). Depending on the fit and on the assumed population size, 12% to 32% of new human amino-acid changes fall below an approximate drift threshold.⁵
5. John Sanford's "one million to one" turns one model estimate into a general ratio. His 2005 and 2014 books give the ratio of harmful to beneficial mutations as one million to one, citing Philip Gerrish and Richard Lenski's 1998 paper, and say beneficial mutations are too rare to measure.⁶ That paper did infer that "roughly one in a million" mutations is beneficial. It solved a model that allows for drift and for competition among beneficial mutations, using three fitness jumps in one E. coli population, and it flagged two assumptions, one of which it said looked false.⁷ The model estimates the total beneficial rate, so the weakness is in its assumptions, not in what it set out to count. Gerrish later wrote that the method carried a prior assumption about the rate's order of magnitude, that a second peak at a much higher rate had gone unreported, and that the same data allow "a much higher estimate".⁸ Other methods, in other strains and population sizes, gave beneficial rates about a thousand times higher (Part 4). In the two significance-tested virus sets with beneficial mutants, the beneficial share is tens of thousands of times above one in a million. Sanford's other source, Bataillon 2000, is about the weak power of one experimental design, not the rate. A 2018 paper by William Basener and Sanford attaches the million-to-one ratio to a reference whose title, journal and pages are Bataillon's (Part 6).
6. Michael Behe makes a different claim, and fitness tables cannot settle it. Behe says beneficial mutations are frequent, but that most of them work by damaging or breaking an existing function.⁹ A fitness assay records growth, not mechanism. The frequency half of his claim matches the laboratory data. Whether most of those beneficial mutations broke something is a question the studies reviewed here do not tally.
7. Below about 0.02%, the studies reviewed here do not resolve the sign of any single mutation's effect, and neither side may fill that zone with a measured number. A writer who says mutations there are almost all harmful, and a writer who says they are neutral or balanced by beneficial ones, are both relying on a model. Fisher's 1930 model predicts that the smallest changes help almost half the time,¹⁰ but that is a model, not a measurement. Parul Johri and colleagues found that, in their human exon data and simulations, a rare weak or moderate beneficial class could not be told apart from none.¹¹

Verdict.  The measured data agree with the young-earth claim that most mutations with an effect are harmful, but standard evolutionary genetics expects the same, so that agreement does not decide between them.  They agree with Behe that beneficial mutations in the laboratory are common enough to observe.  They contradict Sanford's one-in-a-million ratio as a general rule:  its one real source is a single model estimate whose assumptions its authors flagged and its first author later revised, and both the small-benefit rate estimates and the significance-tested virus sets reviewed here sit far above it.  They do not establish what happens below the resolution of the methods reviewed, and the article's companion pieces on Genetic Entropy and Population Genetics take up what that zone means for long-term decline.

This article owns the parameter evidence:  the measured shares and rates, what each method can see, and how each side's numbers compare with them.  The mathematics of the drift barrier is in Population Genetics;  what the shares imply for genomic decline is in Genetic Entropy;  how often a beneficial change builds a new molecular function is in the Observed Evolution and New Genes articles.

Part 1: The reference tables

How to read the tables

Each row is one study, with its own denominator.  The rows are not averaged, because they do not measure the same thing.

1. Denominator. "48 random substitutions" means 48 mutants made one at a time. "37 lines" means 37 mutation-accumulation lines, each carrying an unknown number of mutations, so a line that got worse may hold one bad mutation or several, and a line that got better may hold good and bad ones that partly cancel. "8,970 fitness values" means estimates for variants seen in a growing population, not mutants built one by one.
2. Readout. Virus and microbe studies measure growth or competition in a laboratory. Gene scans often measure something narrower: drug resistance, fluorescence, or a protein's activity. A change that raises resistance to one antibiotic level is not thereby a better organism. Human estimates are not measurements of single mutations at all; they are fits of a model to the frequencies of variants in living people, under an assumed population history.
3. Floor. "No detectable effect" is never "no effect." Each row says what the method could see.
4. Status. "Counted" means the authors classified each mutant or line by a test. "Fitted" means a class share is a parameter of a model. "Ascertained" means the design was built to find one class, so the sample cannot give the share of the other classes. "Derived" means arithmetic in this article, with the script that does it. "Restated" means a later paper's summary, used where the original could not be read.

Table 1. Single mutations made and tested one at a time

Two further studies counted variants rather than engineered mutants.  Rafael Acevedo and colleagues followed poliovirus populations through seven passages and estimated 8,970 fitness values from changes in variant frequency;  944 were above 1 and 145 were significantly beneficial at a 5% false-discovery rate.²⁰  Lydia Robert and colleagues watched about 20,000 new mutations arise in single E. coli cells and report that "1% of mutations were lethal" and that non-lethal ones were "dominated by quasi-neutral mutations with an average cost of 0.3%".²¹  Only the abstract of the second could be read.

Table 2. Gene-wide scans of single proteins and RNAs

Table 3. Mutation-accumulation lines and related designs

These count lines, or fit a model to the spread of lines.  None gives the share of single mutations in each class.

Table 4. Rates of beneficial mutation in microbes

U_b is the rate of new beneficial mutations per cell per generation.  Each is limited to the effects its method could count.

Table 5. Human estimates from variant frequencies

All are fits of a model to the frequencies of amino-acid-changing variants, with a population history fitted to silent variants.  Bins are on each paper's own scale;  the conventions are not interchangeable (Part 5).

Part 2: One mutation at a time

The most direct way to sort mutations into classes is to make them one at a time, put each into an otherwise identical genome, and measure the result.  It has been done for whole small viruses and for single genes, and a related design followed spontaneous harmful mutations in yeast one by one.  In these designs each mutation is tested on its own, so its class does not have to be inferred from a line or a population.  They are also the measurements most open to the charge that the test environment sets the answer.

Small viruses: a fifth to two-fifths lethal

Five studies, most of them from Santiago Elena's and Rafael Sanjuán's groups in Valencia, made random single-letter changes in six small virus genomes and measured how fast each mutant grew (Table 1).  The lethal share ran from 20% in the DNA phage φX174 to 40.9% in tobacco etch virus.  Viable mutants lost about 10% to 13% of their growth rate on average.  Pilar Domingo-Calap and colleagues drew the general lesson:  "It seems therefore that high mutational sensitivity is a general property of viruses with small genomes".¹³

The lethal call is not equally secure in every study.  In each, a mutant counted as lethal when no live virus could be recovered after repeated attempts.  Rafael Sanjuán's 2010 review of the five datasets says that for the vesicular stomatitis virus set "lethality was less well-demonstrated" because the extra controls run for the other viruses "were not carried out in the VSV study".⁵⁵  The 39.6% figure is therefore the least checked of the six.

These genomes are small and densely packed with protein-coding sequence.  The lethal shares measure how often a random change breaks a compact genome.  They do not say what share of mutations in a large genome with much non-coding DNA is lethal, and this article does not use them for that.

Small viruses: beneficial mutants are few, and their number depends on the virus's history

Beneficial mutants were rare in every virus set.  The vesicular stomatitis virus set had 2 of 48 random mutants beneficial.  Sanjuán and colleagues were surprised, because, as they wrote, "It is generally accepted that beneficial effects are ≈1,000-fold less common that neutral and deleterious ones".  They gave a reason:  the virus was built from two strains, with its G gene from a different strain than the rest, so there were "many different possible ways to optimize such genomes", and the virus's adaptation to the laboratory was "minimal".¹  Carrasco, de la Iglesia and Elena found no mutant beneficial at 95% confidence among 66 in tobacco etch virus, and one at 90%, tested in its natural host plant.  They suggested that the host "imposes all kind of strong selective pressures on the virus", unlike the cell cultures used for the animal virus.¹²  Peris and colleagues deliberately used a phage strain already adapted to the laboratory, because doing so "minimizes the fraction of beneficial mutations".  They still found two significantly beneficial mutants out of 100, and added that "the actual fraction might be higher, since mutations of small effect are difficult to detect."¹⁴

So in the three sets that tested every mutant for significance, the beneficial share runs from 0 to about 4% of mutants, and from 0 to about 6% of the mutants that had any detectable effect.⁵  In Elizabeth Visher and colleagues' influenza set, 7 of the 89 viable mutants that could be measured fell in a "weakly beneficial" growth band of 105% to 115% of wild type, but the authors did not test those values for significance and warn that many were "not statistically different from 1".  Their published classes add to 89 of 90 viable mutants because one, HA-8, could not be measured despite repeated attempts.¹⁵  Among the significance-tested sets, the beneficial share is highest where the virus was least adapted to the test conditions and lowest where it was best adapted.  Both facts matter.  A critic may say the higher figures are inflated by poorly adapted laboratory strains.  The same data show that even a well-adapted phage, tested by a strict rule, produced beneficial mutants at a rate of a few per hundred.

Two designs do not classify beneficial mutants at all.  Domingo-Calap's φX174 and Qβ study treated every mutant that grew faster than the wild type as part of the no-effect group:  such mutants "were assumed to be neutral or beneficial", and the analysis went on, in their words, "Neglecting beneficial mutations".¹³  A zero there is a choice of model, not a measurement.

Yeast: a screen for harmful mutations

Dominika Wloch and colleagues found a way to score spontaneous harmful mutations individually in yeast.  A diploid cell's four spores each grow a colony;  a new harmful mutation in one copy of a gene shows up as two slower or missing colonies among the four.  The screen was built to find exactly that:  "Our goal was to identify diploid clones that acquired a deleterious mutation in one locus only", recognised by two colonies that "grew slower".¹⁹  Of 69 spontaneous mutations found this way, 20 were lethal and 49 slowed growth, mostly by 1% to 5%.¹⁹  The authors were explicit about the lower limit:  "the rate and distribution of very small effects could not be determined".¹⁹  Because the 69 were selected as harmful, they cannot give the share of new mutations that are beneficial, and the 20 lethal mutations are 29% of the harmful mutations the screen could catch, not of all new mutations.  Faster growth was noticed only incidentally:  among the induced mutations, two mutants grew faster than the wild type (by 1.5% and 2.6%) and were excluded from the analysis.¹⁹

Two later papers say Wloch's study found nearly 2% of mutations beneficial.  Sarah Joseph and David Hall wrote that "Wloch et al. (2001) found slightly <2% of mutations were beneficial in their haploid MA experiment",³ and Paul Sniegowski and Philip Gerrish's 2010 review repeats "almost 2 per cent".⁸  The Wloch paper read for this article reports no such figure, and its design, a screen for harmful mutations, could not yield one.  Its only faster-growing mutants are the two induced ones it set aside.  Either the restatements rest on a calculation not printed in the paper, or they are wrong.

Bacteria: neutral at one floor, harmful at a lower one

The E. coli experiment Sanford cites, by Elena and colleagues in 1998, inserted transposons at random into a clone that had already evolved for 10,000 generations in the laboratory, and measured each mutant against its unmutated parent.  Of 226 insertion mutants, "at least 80%" were significantly harmful and "None of the mutations conferred a significant advantage";  the one mutant that first looked beneficial proved slightly harmful when retested 30 more times.¹⁷  A transposon insertion often disrupts the gene it lands in, so this is among the most disruptive kinds of mutation.  Zero significant beneficial calls among 226 random insertions puts a 95% upper bound of about 1.3% on the chance that a random insertion would get such a call in that assay, if the insertions are a fair sample.⁵⁶  It says nothing about benefits too small for the assay to detect, and it cannot reach one in a million.  Romain Gallet and colleagues, Elena among them, later took three of those insertion mutants "identified as neutral using the standard plating method" and re-measured them by flow cytometry, a method that estimated their mean selection coefficients to a precision of about 0.02%.  All three were harmful, by 1.2%, 1.7% and 0.3%.⁴  The same pattern appears in Salmonella.  Lind, Berg and Andersson measured 126 single changes in two ribosomal-protein genes "with high sensitivity" and found that "most mutations (120 out of 126) are weakly deleterious and the remaining ones are potentially neutral."  Silent changes, which do not alter the protein, had effects similar to those that did.¹⁶  In each of these retests, a finer method moved some mutations that had been scored neutral into the mildly harmful column.  That is a real pattern in the studies reviewed here, and it runs in the young-earth direction, though it is also what any population geneticist expects of random changes to a working genome.

It runs only so far.  Gallet's team also found that a single mutation's measured effect varied between replicate cultures more than chance allows, and concluded that "selection coefficients are best understood as being distributed, representing a limit on the precision with which selection can be measured".⁴  Below that limit, a mutation does not have one fixed effect that a better instrument could read.

Bacterial genes in their native place

The single-gene study closest to natural conditions is a second one from Dan Andersson's laboratory.  Lind, Arvidsson, Berg and Andersson put 156 single-base changes into three Salmonella genes that the cell needs to grow on the sugar arabinose, each change at the gene's own place on the chromosome, and grew the mutants on arabinose.  Their assay "allowed detection of fitness differences of |s| > 0.004", that is, 0.4%.  All 47 silent changes were indistinguishable from the wild type.  Of the amino-acid changes, 33% to 56% per gene were too small to detect, and the authors call that "an upper limit for the fraction of mutants that are nearly neutral".¹⁸  About 56% were harmful, some nearly as harmful as deleting the gene.¹⁸  Four amino-acid changes raised fitness.  The authors' reading is careful:  "several percent of random mutations might be advantageous when the mutated genes are under strong selection, but the few mutations found here makes estimates of frequency uncertain (f = 2.6%, f > 0.9%…)".¹⁸  In this design the genes were under selection in the test medium and the mutations sat in their normal place.  Among the single-mutation sets reviewed here it is the closest to natural conditions, and its beneficial share, a few percent with a lower bound near 1%, rests on only four mutants.

Whole-gene scans

Deep mutational scanning makes a large library of single changes in one gene, sometimes every possible one, and measures them together by sequencing (Table 2).  What it measures is usually one readout, such as drug resistance, fluorescence or growth in one condition, not the organism's lifetime fitness.  The scans agree with the virus sets on direction.  Most changes that matter are harmful, the distribution often has a second peak near complete loss of function, and a minority of changes improve the measured trait.  In TEM-1, an enzyme that breaks down penicillin-type antibiotics, 7.0% of 5,212 missense mutations raised resistance to ampicillin beyond the measurement error.²²  In a yeast transfer-RNA gene at its native site, 42% of all 207 possible single changes were harmful and 1% beneficial.²³  That 1%, about two mutants, used an uncorrected test at the 5% level.  If the 57% of mutants with no significant effect were all truly neutral, about three beneficial calls would be expected by chance alone.⁵  That makes the 1% provisional.  It does not show that the two calls are false;  a corrected test or a replicate would be needed to settle them.  In green fluorescent protein, "at least 75% of mutations had a deleterious effect on fluorescence".²⁴

Three cautions apply to the scans.

1. The readout is not fitness. Ampicillin resistance at one drug level, fluorescence and protein stability are each one property. A change that raises one may lower another. Montañez, Marks, Fernandez and Sanford argue that where one stretch of DNA serves several codes at once, a change that helps one is likely to hurt another, so single-readout beneficial shares overstate the true share.⁵⁷ Their argument is a calculation, not a measurement, and how much DNA serves several codes is itself disputed.
2. The environment changes the answer. Julia Flynn and colleagues measured all 14,160 amino-acid variants of the yeast chaperone Hsp90 under standard growth and five stresses. "Multiple variants provided growth advantages under individual conditions; however, these variants tended to exhibit growth defects in other environments."²⁶ Claudia Bank and colleagues had earlier found the same in a part of the same gene, and warned that their "wt-like" class, within 0.4% of wild-type growth, "is not necessarily the same as a neutral class of mutations."²⁵
3. Studies score by different rules. Reeb and colleagues compared 22 published scans of 18 proteins. Beneficial changes were the majority in only 3 of 22 studies, and in the other 19 harmful changes outnumbered beneficial ones by 1.5 to 22.5 times. Each study scored its own readout on its own scale.²⁷ The scans cannot be pooled into one percentage.

None of this makes the scans meaningless.  Within one gene, one readout and one condition, they are the most complete counts among the studies reviewed here, and most of them show both that most changes are harmful and that improving changes are not vanishingly rare.

Part 3: Mutation-accumulation lines

A mutation-accumulation experiment starts many lines from one ancestor and passes each through a bottleneck of one individual, or one cell, every generation, so that selection is almost powerless and mutations pile up as they arise.  After tens or thousands of generations, the lines are tested against the ancestor.  The method measures spontaneous mutations of every kind, in a whole organism, often over its whole life cycle.  Its weakness is that it sees lines, not mutations.

What the method can and cannot count

A line that got worse may carry one bad mutation or five.  A line that did not change may carry a good and a bad one that cancel.  The usual analysis, developed by A. J. Bateman and Terumi Mukai and later given likelihood versions by Peter Keightley, infers a mutation rate and a mean effect from the decline in the lines' average and the growth of the spread between them.  It gives a lower bound on the number of mutations with effects and an upper bound on their typical size.  Mukai, Chigusa, Mettler and James Crow wrote of their fruit-fly estimate that "it is not possible to set any meaningful upper limit.  But it is clear that the rate is much higher than the lethal rate, by a factor of at least 10".²⁸  Brian Charlesworth's group put the limit bluntly:  "it is virtually impossible to detect individual mutations with very small effects on components of fitness."⁵⁸

The beneficial side is the hardest to see.  Thomas Bataillon simulated the standard designs in 2000 and concluded that "the power of MA, designs to detect such mutations is probably quite low."⁵⁹  This is a statement about the instrument, not about how many beneficial mutations exist.

Animals: mostly decline, with a disputed positive tail

Fruit-fly and nematode lines decline in fitness, and the inferred effects are mostly harmful.  Fry, Keightley, Heinsohn and Nuzhdin repeated Mukai's fly design with control lines run at the same time.  They found fewer mutations with larger effects than Mukai had, and "were able to reject" his assumption that all mild mutations have equal effects.²⁹  In C. elegans, Keightley and Armando Caballero found effects on lifetime productivity "inferred to be exclusively negative although the upper limit for the proportion of mutations increasing productivity was 28%."³⁰  Estes, Lynch and colleagues estimated that "only a small fraction, perhaps ≪1%, of the mutations in complex sequence have detectable effects on laboratory fitness."⁶⁰  Davies, Peters and Keightley, using a strain in which the number of induced point mutations could be counted, reported that "only about 4 percent of the deleterious mutations fixed in each line were detectable.  The remaining 96 percent, though cryptic, are significant for mutation load".⁶¹  Only the abstract of that paper could be read.

Some animal lines got better.  In Sarah Schaack, Michael Lynch and colleagues' water fleas, 8.1% of the lines assayed improved significantly in competitive ability, against 67.6% that declined.³¹  Those are lines, each holding many mutations.

The largest positive estimates come from fits that let the effect distribution run both ways.  A recent test of such fits is Crombie and colleagues' 2024 C. elegans study, which shuffled 169 known mutations among 517 lines by repeated crossing, so that each mutation's effect could be estimated separately.  A two-sided model put 42.6% of the non-neutral mutations on the positive side.  The authors did not accept it.  Pooling mutations that travel together made the inferred distribution "increasingly negative-skewed and leptokurtic", and they concluded "that the conventional wisdom—most mutations have effects near 0, a handful of mutations have effects that are substantially negative, and mutations with positive effects are very rare—is likely correct, and that unless it can be shown otherwise, estimates of the distribution of fitness effect that infer a substantial fraction of mutations with positive effects are likely confounded by linkage disequilibrium."³⁸  They also say their advanced-intercross set was barely larger than the number of loci, so "there simply is little power" to pin the effects down.³⁸  Their critique is an argument from their own design, which was built to break up linkage;  it gives a reason to doubt other two-sided fits, not a demonstration that each of them is wrong.

Yeast: high beneficial shares, with the authors' own warnings

Yeast lines give some of the highest beneficial shares among the mutation-accumulation studies reviewed here, and the papers that report them also give strong reasons for doubt.

Sarah Joseph and David Hall grew 151 diploid yeast lines for about 1,012 generations.  The lines lost fitness on average, yet "5.75% of the fitness-altering mutations accumulated were beneficial", after correcting an uncorrected estimate of 12.5% with a 95% interval of 0.8% to 38%.  The figure is a maximum-likelihood parameter fitted to the 151 lines' growth rates, not a count of mutations classified one by one.^{3 3}  They listed three reasons the figure might be too high.  First, the growth assay used a complete medium in which "several metabolic pathways, such as those involved in amino acid synthesis, are not required", so breaking them could help in the flask and harm in nature.  Second, "the ancestral strain used in our experiment may have been poorly adapted to the experimental conditions".  Third, they measured heterozygotes, and "If deleterious mutations are more likely than beneficials to be recessive, then they would appear underrepresented".³  They also argued against the simplest dismissal.  If the real share were 0.1%, then halving the frequency of harmful mutations "increases the proportion that are beneficial to only 0.2%."³

Two follow-ups raised the figure and kept the warnings.  After 1,050 more generations, Hall and colleagues estimated "that 13 % of the mutations accumulated during this study are beneficial", while naming a low-fitness ancestor, a benign medium and overdominance as alternative explanations.³³  W. Joseph Dickinson, with a different design, concluded "that almost a quarter of the significant fitness changes fixed by drift were improvements."³⁴  Then Hall and Joseph measured four parts of the yeast life cycle in the original lines.  No line had better spore survival than the ancestor, and the authors wrote that "the accumulation of recessive deleterious mutations may have inflated our previous estimate of the proportion of beneficial mutations."³²  Clifford Zeyl and Arjan de Visser's diploid lines needed no beneficial class:  adding one "did not improve the fit to the data".³⁵

So the yeast figures are real measurements of heterozygous growth in one rich medium.  They are not measurements of a beneficial share of all new mutations in nature, and their own authors say so.

Plants, algae and bacteria

Ruth Shaw's Arabidopsis lines gave "approximately symmetric" effects on reproductive traits,³⁹ and the model that Shaw, Geyer and Shaw built to fit such data found "distributions of mutational effects broadly spanning zero, such that roughly half the mutations reduce reproductive fitness."⁶²  Only the abstract of the second paper could be read.  In the green alga Chlamydomonas, Böndel and colleagues found that "Of mutations with absolute fitness effects exceeding 1%, about one-sixth increase fitness in the laboratory environment", while a two-sided model put about 80% of all mutations on the positive side, which they called "surprisingly high".³⁷  These are the strongest counter-examples to "beneficial mutations are rare" among the studies reviewed here.  They are also two-sided model fits to lines.  Crombie's team argues that such fits are prone to confounding by linkage;  Böndel's recombinant lines come from one round of crossing with the ancestor, which reshuffles mutations less thoroughly than Crombie's repeated intercrossing, and whether the critique applies to them with the same force has not been tested in the work reviewed here.

In the bacterium Burkholderia cenocepacia, Marcus Dillon and Vaughn Cooper sequenced every line, so they knew the 290 mutations.  In a rich medium 17 lines got worse and none better.  In a minimal medium 13 got worse and 4 better.³⁶  From those four lines they derived a beneficial rate of 1.68 × 10⁻⁵ per genome per generation with a mean benefit of 1.3%, under their stated assumption that one mutation sets each line's fitness, although each line carried about 6.7 mutations.³⁶  The same lines were worse, unchanged or better depending on the medium.

Part 4: How often beneficial mutations arise

A different set of microbial experiments asks how often beneficial mutations arise, not what share of a sample they make up.  They follow a large population as it adapts and infer the rate, U_b, at which new beneficial mutations appear (Table 4).  This is where the phrase "one in a million" comes from, and also where later work with other methods gave much higher figures.

Gerrish and Lenski 1998: the source of "one in a million"

Philip Gerrish and Richard Lenski's 1998 paper is mainly a theory of how beneficial mutations compete in an asexual population, a process called clonal interference.  At the end of one section they apply their model to one population of Lenski's long-term E. coli experiment, during its first adaptation to the laboratory medium.  That population showed "three sudden fitness increases during ∼1400 natural generations", which they turned into an average substitution rate of 0.002 per generation and an average gain of 0.1 per substitution, with an effective population size of 3.3 × 10⁷.  The model allows for beneficial mutations that are lost to drift and for those outcompeted by better ones.  Solving its two equations for those observations gave a mean-effect parameter of 35 and a total beneficial rate of 2.0 × 10⁻⁹ per replication.  Then:  "Given that the genomic mutation rate of E. coli is approximately 3 × 10⁻³ mutations per replication (Drake, 1991), one can infer that the proportion of mutations that are beneficial is roughly one in a million."  They added at once that "these estimates depend on (i) the assumption of an exponential distribution of beneficial mutational effects, and (ii) the assumption that λ and μ remain constant even as mean fitness increases", and that the fitness record suggested assumption (ii) "is false if the environment is constant."⁷

The figure is real, and Sanford cites it accurately for its order of magnitude.  Its limits lie in its data and assumptions, not in what it set out to estimate.

1. It is a model estimate from three events. The rate is not counted; it is what the model needs in order to produce three sweeps of about 10% in about 1,400 generations. With so few events, the answer leans heavily on the model's form: an exponential distribution of benefits, and a rate and distribution that stay constant while fitness rises. The paper says the fitness record suggests the second assumption "is false if the environment is constant."⁷ A different distribution of effects, such as one with many small benefits, could fit the same three sweeps with a different rate.
2. It is a share of all mutations, not a ratio to harmful ones. The denominator is the total mutation rate, which includes the neutral ones.
3. It is one population, in one medium, early in its adaptation. It says nothing directly about other species, other genomes or other environments.
4. Its first author later argued that the value was too low. In 2010 Paul Sniegowski and Gerrish wrote that the 1998 estimate, and a later one by the same method, came from "a likelihood model that accounted for both drift and clonal interference". The trouble was elsewhere: the model "made an a priori assumption that Ub was roughly of the same order of magnitude as 1/2N ln (Ns/2); it is no surprise, therefore, that the highest likelihood peak obtained was in this vicinity." A second peak "at much higher Ub and lower average selective advantage" had been observed and not reported, "most likely due to the model's a priori assumptions about Ub". They concluded that the data used for the very low estimate "can be re-analysed using this model", a newer deterministic model of their own, "to obtain a much higher estimate of Ub consistent with other, more recent estimates".⁸ The 2010 text read here prints no reanalysed number. The 1998 paper itself describes solving two equations rather than a likelihood search; the 2010 description covers it together with Rozen and colleagues' 2002 estimate.

The rate rises as smaller benefits become visible

Later experiments estimated the same quantity with methods able to see smaller benefits, in other strains, population sizes and models.

1. Imhof and Schlötterer tracked neutral markers in ten E. coli cultures and counted 66 sweeps. They estimated 4 × 10⁻⁹ beneficial mutations per cell per generation, with a mean benefit of 2%. Sweeps worth less than 1% were left out because "most of them could not be discriminated from experimental errors."⁴⁰
2. Perfeito, Gordo and colleagues used smaller populations, about 10⁴ cells, so that small beneficial mutations were not swamped by large ones. They "found a rate on the order of 10⁻⁵ per genome per generation, which is 1000 times as high as previous estimates, and a mean selective advantage of 1%."⁴³ Only the abstract could be read; Sniegowski and Gerrish restate the rate as about 2 × 10⁻⁵ and explain the jump as "the detection of abundant mutations of small effect that were being outcompeted in larger populations."⁸
3. Michael Desai, Daniel Fisher and Andrew Murray fitted a model of competing beneficial mutations to yeast populations of three sizes and obtained 2.4 × 10⁻⁵ with a typical benefit of 2%, a figure conditional on that model.⁴⁴
4. Sasha Levy and colleagues tracked about 500,000 barcoded yeast lineages. Benefits over 5% arose at about 10⁻⁶ per cell per generation. Including benefits of 2% to 5% gave an inferred rate about 50 times higher, but those lineages carried mutations that were "mostly pre-existing", already present before tracking began, so that figure is a model inference rather than new mutations seen arising. They stated the general lesson: "Reported beneficial mutation rates depend on the range of fitness effects that can establish and be detected."⁴⁵ Below 2%, a new mutation in their population was "extremely unlikely to establish" at all.

Sniegowski and Gerrish turned the higher rates into shares by assuming that the total mutation rate of E. coli and yeast is about 3 × 10⁻³ per genome per generation.  On that assumption they "imply that almost 1 per cent of all mutations in experimental populations of these organisms are beneficial."⁸  The same assumed denominator puts the E. coli and yeast figures above between about 1 in 750,000 new mutations (Imhof) and about 1 in 150 (Perfeito) or 1 in 125 (Desai).⁵  That 5,000-fold spread comes from studies that differ in strain, adaptation history, population size, model and detection limit together, so it cannot be put down to detection alone, though Levy's team and Sniegowski and Gerrish both name detection as a main cause.  Dillon's Burkholderia rate is left out of this division, because no total mutation rate for that species is assumed in the sources used here.

Adaptation shrinks the beneficial supply

Every one of these numbers belongs to a particular genome in a particular place.  Alejandro Couce and colleagues inserted transposons into every gene of clones from Lenski's long-term experiment.  The ancestor had 0.9% of insertions beneficial at s above 0.03, against 0.5% in clones after 50,000 generations;  a finer scan gave 6.8% in the ancestor against 4.3% and 3.2% after 2,000 and 15,000 generations.⁴⁶  And benefits did not travel:  "Only 5.9% of the mutations beneficial in the ancestor are still beneficial at 2,000 generations, with most becoming effectively neutral (76.9%) and some deleterious (17.2%)".⁴⁶  Sanford is right that the beneficial share falls as an organism becomes better adapted.  Couce's clones show it directly, and it is what adaptation theory predicts.

Bataillon and Bailey, reviewing these experiments in 2014, put both sides of the laboratory question.  "Beneficial mutations are not so rare that they cannot be detected when looked for in evolution experiments, and depending on the particular selection environment, beneficial mutations can even be quite numerous."  And at once:  "It could be argued that these data represent the DFE of extremely maladapted populations, important only in the artificial environment of the lab."⁴¹  H. Allen Orr, writing a year earlier than Sniegowski and Gerrish, could still say:  "mutations are rare and beneficial mutations are extremely rare."⁶³  Per cell division that is true:  even a rate of 2 × 10⁻⁵ means one beneficial mutation in 50,000 divisions.  It is not a statement that beneficial mutations are a millionth of all mutations.

Part 5: Human estimates from variant frequencies

The human studies reviewed here do not test mutations one at a time.  They infer effects from the frequencies of amino-acid-changing variants in samples of living people (Table 5).  Strongly harmful variants are kept rare by selection;  weakly harmful ones drift to moderate frequencies;  neutral ones should behave like silent variants.  A model of population history is fitted to the silent variants, which are treated as neutral, and a model of selection is then fitted to the amino-acid variants.  If silent variants are themselves under weak selection, the reference shifts with them.  The result is a distribution of effects for new mutations, inferred rather than observed.

What the fits agree on

The fits agree on a broad shape.  A large minority of new amino-acid changes have effects too small for selection to see in human populations, a broad middle has effects between 0.01% and 1%, and a substantial share are strongly harmful.  Boyko and colleagues put it as "27–29% of amino acid changing (nonsynonymous) mutations are neutral or nearly neutral (|s|<0.01%), 30–42% are moderately deleterious (0.01%<|s|<1%), and nearly all the remainder are highly deleterious or lethal (|s|>1%)."⁴⁸  Gregory Kryukov, Len Pennacchio and Shamil Sunyaev estimated that about 20% of new missense mutations destroy the protein's function, about 27% are effectively neutral, and "the majority (53%) of all de novo missense mutations are, in fact, mildly deleterious".⁵¹

The script that accompanies this article checks the printed parameters against the printed tables.  Eyre-Walker's gamma (shape 0.23, mean N_e·s of 425) reproduces his five class shares to within one percentage point;  Boyko's (shape 0.184, scale 8,200, with his stated population size of 25,636) reproduces his Table 3 to within 0.1 point;  and Kim's (shape 0.186, scale 875) matches the other four bins of Kim's Table 3 once his unstated ancestral population size is calibrated on the first bin, at about 12,300.⁵  That calibration is a consistency check of the printed table, not an independent estimate of population size.  The tables are internally consistent.  That does not make them measurements.

Where they disagree, and why

1. The strong tail is extrapolated. Adam Eyre-Walker, Megan Woolfit and Ted Phelps wrote that "we have no direct information about the distribution of fitness effects of mutations with fitness effects of Nes > 100 or Nes < 1", because strongly harmful variants are almost never sampled and very weak ones all look neutral, so their estimate "beyond these limits is therefore a projection based on the assumption that the distribution is well described by a gamma distribution".⁴⁷ The share above |s| = 10⁻² runs from 17.8% (Kim) to 35.5% (Boyko), though Kim's additive s and Boyko's heterozygote s are not guaranteed to be the same biological quantity.
2. Population history moves the numbers. Each fit depends on a demographic model, and the papers show the shares move when the model changes. Kim's fits, using samples of over 1,000 people and a history with recent growth, give 0.38 to 0.84 times as many strongly harmful mutations as Boyko's.⁴⁹
3. The scales differ. Some papers define s on the heterozygote (Eyre-Walker 2006, Boyko 2008, Kryukov 2007), some on the homozygote (Fay 2001, Keightley & Eyre-Walker 2007), and Kim 2017 states only that effects are additive. The same bin edge is a factor of two apart on different scales. Table 5 keeps each paper's own scale.
4. Most fits have no beneficial class. Eyre-Walker 2006, Keightley & Eyre-Walker 2007, Fay 2001, Kryukov 2007, Boyko's best fit and Kim 2017 model only harmful and neutral mutations. Kim's team noted what that does: their method "would place these mutations at the neutral point mass", and their neutral class "might not reflect truly neutral mutations, but rather slightly beneficial mutations that behave effectively neutral under the historically small human population size".⁴⁹ A model without a beneficial class does not measure zero beneficial mutations. It assumes zero.

The beneficial estimates that exist

When a beneficial class is added, the estimate depends on what is assumed about it.  Boyko's fits put 1.86%, 0.23% or 0.05% of sites in a beneficial class, as the assumed strength of benefit was raised from weak to strong.⁴⁸  Christian Huber and colleagues fitted Fisher's geometric model and estimated "that 14% of new nonsynonymous mutations in humans are beneficial.  The majority (98%) of these beneficial mutations have small selection coefficients, with s < 0.0005".⁵³  Zhen and colleagues, looking for stronger beneficial mutations on top of Huber's distribution, found a best fit near 1.5% at s near 10⁻⁴, but warned that many combinations fit equally well:  "the two parameters are not separable."⁵⁴  The 1.5% is read from their figure, not printed.

Parul Johri, Susanne Pfeifer and Jeffrey Jensen then asked whether human data can detect a rare beneficial class at all.  They jointly fitted population history and selection to 465 long exons, and found that "weak to moderate positive selection is consistent but unidentifiable if rare."¹¹  In their simulations, "when 0.1% or 1% of new mutations are beneficial and the strength of positive selection is weak or moderate ( 2 N e s b = 10 or 100 ), there is almost no difference" in the statistics.¹¹  So, for their exons, summary statistics and simulated cases, a weak or moderate beneficial class of 1% or less left the data almost unchanged.  That is a limit of this kind of fit with these data, not a proof that no human method could ever detect such a class.  Until one does, neither a young-earth writer nor a mainstream one can cite a human fit of this kind as showing that beneficial mutations are absent, or that they are common.

Fixed differences are a different quantity

Estimates of how many amino-acid differences between humans and chimpanzees were fixed by positive selection, such as Boyko's 10% to 20%, are shares of substitutions, not of new mutations.⁴⁸  A beneficial mutation is far more likely to fix than a neutral or harmful one, so a small beneficial share of new mutations can produce a large share of fixed differences.  The two numbers must not be compared as if they were the same thing.  Whether most fixed differences are neutral is argued in the Neutral Theory article.

Part 6: The claims, priced against the tables

John Sanford: "one million to one"

The claim, in his words.  In the 2005 edition of Genetic Entropy:  "I have seen estimates of the ratio of deleterious-to-beneficial mutations which range from one thousand to one, up to one million to one.  The best estimates seem to be one million to one (Gerrish and Lenski, 1998).  The actual rate of beneficial mutations is so extremely low as to thwart any actual measurement (Bataillon, 2000, Elena et al, 1998)."⁶  The 2014 edition keeps the passage with "I believe the best estimates are closer to one million to one".⁶⁴  Its Figure 3d draws the beneficial side as "a reverse image of Kimura's curve, but reduced in range and scale, by a factor of somewhere between one thousand to one million."⁶⁴  Sanford's argument is that beneficial mutations are so rare, and mostly so small, that selection cannot use them to offset the steady input of harmful ones.  What that implies for decline is argued in Genetic Entropy.  The question here is whether the ratio matches the measurements.

What his three sources say.

1. Gerrish and Lenski 1998 does say "roughly one in a million" (Part 4). But it says one in a million of all mutations, not one beneficial for every million harmful ones; it gets the figure by solving a model from three fitness jumps in one population, under two assumptions it flagged; and Gerrish later wrote that a prior assumption built into the method had held the estimate low.^{7 8} Sanford's citation is accurate about the number and leaves out how provisional it was.
2. Bataillon 2000 does not say beneficial mutations are too rare to measure. It reports that one reanalysis of fly lines "fitted a model where 10% of mutations were beneficial", asks whether mutation-accumulation designs could detect them, and answers that "the power of MA, designs to detect such mutations is probably quite low."⁵⁹ That is a statement about the instrument, which Part 3 confirms, not about the rate.
3. Elena and colleagues 1998 found no beneficial mutant among 226 transposon insertions (Part 2).¹⁷ That fits "beneficial mutations are rare", for one of the most disruptive kinds of mutation in an already adapted strain. It bounds the chance of a detectable beneficial insertion in that assay below about 1.3%; it cannot reach one in a million, and it says nothing about benefits below the assay's resolution.

Priced against each study's own denominator.  Sanford's ratio is harmful to beneficial, so the comparable figure is harmful plus lethal mutants against beneficial ones.  Only random samples in which every mutant was tested for significance give that ratio as a count.  In the two such sets with beneficial mutants, the ratio is 16.5 to 1 in vesicular stomatitis virus and 22.5 to 1 in phage f1, and Sanford's one million to one is about 44,000 to 61,000 times more extreme.⁵  Joseph and Hall's yeast lines imply 16.4 to 1, but that is a fitted model parameter, not a count.  The yeast transfer-RNA scan's nominal 42 to 1 and Visher's influenza growth bands are not priced, because neither beneficial class rests on a corrected significance test.  The sets with no significant beneficial call, tobacco etch virus (66 mutants) and Elena's insertions (226), put 95% upper bounds of about 4.4% and 1.3% on the chance that a random mutant in those assays gets a beneficial call.  They are consistent with a high ratio but do not measure one, and they say nothing about benefits too small to detect.  Wloch's yeast mutations are left out, because the screen was built to find harmful ones.  The rates in Part 4, divided by an assumed total mutation rate, give beneficial mutations as 1 in 125 to 1 in 1.5 million of new mutations in E. coli and yeast, the low end coming from large-population studies that see mostly large benefits and model the rest.

Where "one in a million" does have a basis.  Two E. coli estimates from large populations in their first adaptation to the laboratory medium sit near one in a million under the assumed total rate.  Sniegowski and Gerrish describe both, with similar early estimates, as made with effective populations of 10⁷ or more "in strains that had not previously undergone genetic adaptation to the growth environment used".⁸  They are Gerrish and Lenski's 1 in 1.5 million and Imhof and Schlötterer's 1 in 750,000.  Imhof's counted sweeps worth 1% or more;  Gerrish's model inferred the rest from three sweeps.  These are real estimates under their methods and assumptions.  They become an error when read as the share of beneficial mutations in general, or as the ratio of harmful to beneficial among all new mutations.

What he does with the higher figures.  The 2014 edition answers the laboratory reports of frequent beneficial mutations by saying that "a large part (up to 50%) of any microbial genome consists of 'just-in-case genes'" which can be lost with profit in an unchanging laboratory.⁶⁴  That is a fair point about what "beneficial" means in a flask, and Part 3 shows that the yeast authors raised it themselves.  But it concedes that beneficial mutations are measurable and common in the laboratory, against the same chapter's claim that their rate is "so extremely low as to thwart any actual measurement."  The chapter also quotes Bataillon and Bailey's review that "beneficial mutations are not so rare that they cannot be detected when looked for in evolution experiments, and depending on the particular selection environment, beneficial mutations can even be quite numerous", together with its next sentence about "extremely maladapted populations", and concludes:  "These authors clearly understand that beneficial mutations are extremely rare anomalies."⁶⁴  The review raises the maladaptation point as something that "could be argued", and continues:  "However, even if these experiments do represent DFE at the extremes, understanding the DFE of beneficial mutations in maladapted populations is of direct importance".⁴¹  The authors do not say beneficial mutations are extremely rare anomalies.

Sanford's colleagues' working numbers

The modelling papers by Sanford and his colleagues use beneficial fractions far above one in a million, and say so.

1. Basener and Sanford 2018. The paper states: "Gerrish and Lenski estimate the ratio of deleterious to beneficial mutations at a million to one (Gerrish and Lenski 1998b)".⁶⁵ Its reference list gives "Gerrish and Lenski 1998b" as "Estimation of spontaneous genome-wide mutation rate parameters: whither beneficial mutations? Heredity 84:497–501". That title, journal and page range belong to Bataillon's single-author paper of 2000, which gives no such ratio. The paper's own simulations then "make the simplifying assumption that the fraction of beneficial mutations is 0.001", adding that "This fraction of beneficial mutations overestimates the actual rate of beneficial mutations by orders of magnitude."⁶⁵ Their model has no separate class of exactly neutral mutations, so a beneficial fraction of 0.001 and a harmful-to-beneficial ratio of one million to one share roughly the same denominator, and the working value is about 1,000 times the cited one.⁵ It is still below the beneficial shares of all tested mutants in the vesicular stomatitis virus and f1 sets, 4.2% and 2%.
2. Brewer, Smith and Sanford 2013. This simulation of an RNA virus used "10% of all mutations as being perfectly neutral, with the remainder of mutations being 99% deleterious and 1% beneficial", citing Sanjuán and colleagues 2004.⁶⁶ Sanjuán's random mutations were 27.1% neutral and 4.2% beneficial, with 39.6% lethal.¹ The simulation set the neutral share 2.7 times lower and the beneficial share 4.7 times lower than its own source.⁵ Lethal mutations were to be handled "by simply adjusting the rate of 'random deaths'". The first, baseline run "modeled zero random death"; later runs added random loss of 25% or 40% of particles, which the chapter attributes to chance, host defences or drugs rather than to lethal mutations.⁶⁶ None of the runs is described as setting random death to Sanjuán's lethal share. In fairness, Sanjuán called his own beneficial share possibly inflated by the two-strain virus (Part 2), and the chapter itself says that "no one knows the precise shape of the distribution of mutation effects for a given virus."⁶⁶
3. Montañez, Marks, Fernandez and Sanford 2013. This chapter repeats that "beneficial mutations might be as rare as one in a million", citing Elena 1998 and Gerrish and Lenski 1998, and then reports that "more recently some have argued that beneficial mutations might be much more common", citing Joseph and Hall 2004 and Dickinson 2008.⁵⁷ Its own contribution is the overlapping-codes argument in Part 2: a calculation that unambiguous benefits should be rarer than single-readout assays show. Sanford's 2014 book cites it as having "very effectively refuted" the high laboratory rates.⁶⁴ It argues that they overstate the general share; it does not measure a share.

Michael Behe: beneficial by breaking

The claim, in his words.  Behe's Darwin Devolves (2019) does not say beneficial mutations are rare.  It says most of them damage something:  "the great majority of even beneficial positively selected mutations damage an organism's genetic information—either degrading or outright destroying functional coded elements."⁹  His reason is target size:  "the rate of appearance of a beneficial mutation that breaks or degrades a gene is expected to be hundreds to thousands of times faster than a beneficial mutation that has to change a specific nucleotide in a gene."⁹  He calls this the First Rule of Adaptive Evolution, "Break or blunt any functional coded element whose loss would yield a net fitness gain", and adds that it is "a rule of thumb.  It's not an ironclad law about what has to happen."⁹  And he says the problem is frequency, not rarity:  "it's not so much the rarity of constructive mutations that undermines Darwinian evolution—it's the frequency of damaging but helpful ones."⁹

What the tables can and cannot say.  Behe's claim is about what kind of mutation is beneficial, and almost nothing in the tables records that.  A fitness assay measures growth.  It does not record whether the mutation that raised growth broke a gene, retuned one, or built something new.  So the shares in Part 1 neither confirm nor refute the rule.  Three things in the tables bear on it.

1. Many of the high beneficial shares were measured where breaking could be useful: a yeast ancestor in a medium where amino-acid pathways are not needed,³ a virus built from two strains, and bacteria with genes they do not need in a flask. That setting is consistent with Behe's argument and Sanford's "just-in-case genes", but a fitness score does not show that any given beneficial mutation broke something.
2. The frequency side of Behe's claim is supported: beneficial mutations in laboratory populations are common enough to count, at a few per hundred mutants or about 10⁻⁵ per genome per generation where small benefits can be seen.
3. Some beneficial changes leave the gene intact. The four beneficial amino-acid changes in Lind's Salmonella genes and the 7.0% of TEM-1 changes that raised ampicillin resistance are substitutions in working proteins.^{18 22} Behe would count most such changes as modifications of an existing function, not new functions, and the scans do not say which they are. Whether beneficial changes are mostly losses is taken up in Genetic Entropy, in its section on what beneficial mutations do, and in the Observed Evolution articles.

The mainstream reply.  Richard Lenski, whose long-term E. coli experiment Behe draws on, accepts a weaker form of the observation:  "I would tone it down as follows: 'The tendency of random mutation is to degrade genes, and that is sometimes helpful.'"  He rejects the step from frequency to importance as "an unjustifiable extrapolation", arguing that "even if many more mutations destroy functions than produce new functions, the latter category has been far more consequential in the history of life."⁶⁷  That is an argument about importance, not a measured share.  None of the studies reviewed here reports a share of new beneficial mutations sorted by mechanism.

A tension between the two creationist claims.  Sanford says beneficial mutations are too rare to measure.  Behe says damaging but helpful ones are frequent and arrive first.  The laboratory data side with Behe on frequency.  The studies reviewed here do not test the mechanism half.

The mainstream's strong claims, priced the same way

1. "Advantageous mutations are rare." This is the standard review's summary,² and it is true in the sense the review gives it on page 613: in the mutagenesis experiments then available, "the proportion of advantageous mutations was 4%" in one virus, 0% in E. coli, 0% to 15% in φX174, 0% in φ6 and 6% in yeast.² "Rare" there means zero to a few percent of mutations with an effect.
2. "Most mutations are neutral." For the whole human genome this depends on how much of it is functional, which is argued in the Junk DNA and Genome Function articles. For amino-acid changes the fits put only about 12% to 32% below the scale where drift overwhelms selection (Part 5). For compact virus genomes and single microbial genes the measured no-effect share runs from about 20% to 57%. The authors treat those as upper bounds on true neutrality, which holds to the extent that their significant calls are right.
3. "About half of new mutations are beneficial." This rests on two-sided model fits to mutation-accumulation lines (Shaw 2002, Böndel 2019) and counts of significant changes in lines (Dickinson 2008, Hall 2008). Crombie's team concludes from its own reduced-linkage design that such fits are "likely confounded by linkage disequilibrium" unless shown otherwise,³⁸ and Hall and Joseph suspect recessive harmful mutations inflated their own figure.³² Most single-mutation sets reviewed here (Tables 1 and 2) give shares well below half, although 3 of 22 gene scans found a beneficial majority under their own readouts.
4. "Fisher showed that small mutations help half the time." R. A. Fisher's 1930 geometric model does predict that a very small random change has "an almost equal chance of effecting improvement or the reverse", and that for changes much smaller than any deliberate adjustment "the chance of improvement should be almost exactly half."^{10 10} That is a property of an idealised model of a well-adapted organism, in the limit of vanishingly small steps, not a measured rate. Huber's fit of a version of the model to human data gives 14% beneficial over the whole range of fitted effects;⁵³ that does not contradict Fisher's limit, which concerns only the smallest steps. Part 7 returns to what the model does and does not license.

Part 7: The zone the reviewed methods do not resolve

Two different limits

Two separate limits are often run together.

1. The population limit. Selection has less influence relative to genetic drift when a mutation's effect is small compared with the random variation in who breeds. The rough rule is that a mutation behaves as neutral when |s| is below about 1/(2N_e) to 1/(4N_e), where N_e is the effective population size, and the constant depends on whether s is defined on the heterozygote or the homozygote. For humans, with N_e taken as 10,000 to 20,000, that puts the threshold somewhere between about 1.3 × 10⁻⁵ and 5 × 10⁻⁵.⁶⁸ The threshold is a property of the population, not of the mutation, and it is a gradual shoulder, not a wall: selection still acts below it, ever more weakly against drift. The formula and its history are in Population Genetics.
2. The instrument limit. A laboratory can tell a mutant from its parent only if the difference is larger than the assay's error.

The first sets, roughly, how strongly selection can act on a mutation in a population.  The second sets which mutations a given study could measure.  They are different numbers, and the microbial assays reviewed here resolve effects well above the approximate human threshold.

The floors, side by side

Romain Gallet's team, whose precision is the finest reported among the studies reviewed here, doubt it can go much lower:  "Increased sampling effort, larger population sizes, or longer lasting experiments are not likely to resolve this issue.  It is thus unclear how far precision in fitness measurement can be improved."⁴  Grant Kinsler and colleagues state the consequence:  "natural selection can distinguish fitness differences that are orders of magnitude smaller than we can measure in the laboratory, depending on effective population size".⁶⁹  As a scale illustration only, Gallet's microbial precision is roughly 4 to 16 times the approximate human drift threshold, and ordinary assays are 20 to 800 times it.⁶⁸  No such assay has been run on human mutations, so these are comparisons of scale, not measured human limits.

What the gap licenses, and what it does not

What the reviewed studies do not measure.  None of the studies reviewed here resolves the sign of a single mutation's effect when that effect is smaller than about 2 × 10⁻⁴.  Precision of a mean, a standard error, a significance threshold and a model's inference are different things, and none of them, in these studies, sorts individual mutations below that size.  The human fits put 12% to 32% of new amino-acid changes below the human drift threshold, depending on the fit and the assumed N_e (Part 5), but they get that share from the shape of a fitted curve, and the curve has no beneficial side unless one is put in by hand.

What a young-earth writer may say.

1. "Neutral" in a laboratory table means "below this assay's floor", not "no effect." The review the field cites agrees: "it seems unlikely that any mutation is truly neutral in the sense that it has no effect on fitness. All mutations must have some effect, even if that effect is vanishingly small."²
2. In each retest reviewed here, a finer method moved some mutations that had been scored neutral into the mildly harmful column: Elena's apparent-neutral insertions on retest, Gallet's re-measured insertions, and Lind's Salmonella ribosomal genes (Part 2). Davies, Peters and Keightley estimated that 96% of the harmful mutations in their nematode lines were invisible to fitness assays.⁶¹
3. The direction agrees with the gene scans reviewed here, in most of which the changes that move the readout mostly make it worse.

What a young-earth writer may not say.  That the zone is measured to be overwhelmingly harmful, or that it holds a million harmful mutations for each beneficial one.  The studies reviewed here do not measure it.  Sanford's Figure 3d, "a reverse image of Kimura's curve, but reduced in range and scale, by a factor of somewhere between one thousand to one million", is a drawing of an assumption.⁶⁴

What a mainstream writer may say.  The fitted human distributions describe the mass of weak effects well enough to predict the variant frequencies, and the effects in the zone are tiny by definition.  The one theoretical model with a long pedigree points toward balance at the smallest scale:  Fisher's model gives "an almost equal chance of effecting improvement or the reverse" for an "extremely minute" change.¹⁰  And Lind's team found that "slightly advantageous mutations make up a significant fraction of the DFE, but that they often escape detection due to the limited sensitivity of commonly used fitness assays."¹⁸

What these studies do not establish.  They do not show that effects in the zone are exactly zero, or that beneficial effects there balance harmful effects.  Calling a mutation effectively neutral means drift has more influence than selection in a specified population; it does not mean the mutation has no effect.  Fisher's balance is a property of an idealised model, and Johri's team found that a rare weak beneficial class "is consistent but unidentifiable" in their human data.¹¹  A human fit that excludes beneficial mutations cannot independently determine their frequency.  Either side can offer a model for the unresolved range, provided it identifies the assumptions and does not call the result a direct measurement.

The honest description of the zone is that its size is known roughly, its content is not, and both sides fill it with a model.  What the unresolved zone implies for whether genomes decline is argued in Genetic Entropy and is not repeated here.

Objections and responses

1. "The laboratory beneficial mutations are artefacts. Poorly adapted strains, rich media and unneeded genes make breaking things look helpful; in nature the same mutations would be harmful." Partly right, and the laboratory authors say so themselves (Part 3). The beneficial share falls as a strain adapts,⁴⁶ and benefits in one environment often cost in another.²⁶ But the objection cannot bring the share near one in a million. The best-adapted settings in the tables, a phage chosen because it was already adapted to the laboratory, Salmonella genes mutated in place and grown where they are needed, and an E. coli clone after 10,000 generations, gave 2 of 100, 4 of about 109 amino-acid changes, and 0 of 226 insertions. Those are shares of 0% to about 4%, not 0.0001%.
2. "Most 'neutral' mutations are really slightly harmful, so the harmful share is even higher than the tables say." Probably true, and the retests in Part 2 support it. But a lower floor also uncovers beneficial mutations: Sanjuán's and Peris's teams call their beneficial shares lower bounds, and Lind's team found slightly advantageous mutations that "often escape detection".¹⁸ In the two virus sets with significant beneficial mutants, moving every neutral mutant into the harmful column would raise the ratio from 16.5 and 22.5 to 23 and 49 to 1, a factor of about 1.4 to 2.2, not ten thousand.
3. "Gerrish and Lenski's estimate is the realistic one, because it comes from a large population where only real winners count." For the question of which beneficial mutations take over a large population, large-population experiments are the relevant ones. Gerrish and Lenski's model does try to answer the other question, how many beneficial mutations arise, by allowing for those lost to drift and competition. But in a large population small benefits rarely leave a trace, so the model has to supply them from its assumptions, and three sweeps cannot pin those assumptions down. The authors flagged two of them,⁷ and Gerrish later wrote that a prior assumption about the rate had held the estimate low.⁸
4. "Beneficial mutations are common: Shaw's plants and Böndel's algae show about half." Those figures come from two-sided model fits to mutation-accumulation lines. Crombie's team, testing such fits with a design built to reduce linkage, concluded they are "likely confounded by linkage disequilibrium" unless shown otherwise.³⁸ That is a reason for caution, not a refutation of each fit. Most single-mutation sets reviewed here, which do not have that problem, give a few percent.
5. "Viruses are not people. A 40% lethal share says nothing about the human genome." Agreed. This article uses the virus figures only as measurements of compact genomes, and says so in Part 2.
6. "Human fits show a quarter to a third of amino-acid changes are effectively neutral, so mutation is not a problem." The share is conditional on the fit, the scale and the assumed population size, and runs from about 12% to 32% (Part 5). What any of these shares implies for long-term decline is the subject of Genetic Entropy.
7. "Behe is right that beneficial mutations break things, so counting them proves nothing for evolution." The tables count frequency, not mechanism, and Behe himself says the problem is "the frequency of damaging but helpful ones", not their rarity.⁹ The counts therefore support the frequency half of his claim and are silent on the mechanism half. Some counted benefits are substitutions in intact proteins, which Behe would mostly call modifications of function.
8. "Fisher's geometric model proves that half of very small mutations are beneficial." It shows that half would be in an idealised model of a well-adapted organism, at vanishingly small sizes.¹⁰ None of the studies reviewed here tests it at the sizes concerned. A fit of a version of the model to human data gives 14% beneficial over the whole fitted range of effects,⁵³ which neither confirms nor contradicts the limit for the smallest steps.
9. "Overlapping codes make a mutation that is beneficial in every respect far rarer than any single-readout scan shows." The logic is sound for scans that measure one property of one protein.⁵⁷ Whole-organism fitness assays, such as the virus, yeast and Salmonella competitions, already integrate every function the organism uses in the test, and several of them still find beneficial mutants at a few percent. How much DNA serves several codes is disputed and is argued elsewhere.
10. "Sanford's 'one million to one' was only an illustration of rarity." He called it "The best estimates" in 2005 and "the best estimates" in 2014,^{6 64} and a 2018 paper by Basener and Sanford presents it as Gerrish and Lenski's estimate.⁶⁵ It is presented as a measurement.
11. "The mainstream review says 'advantageous mutations are rare', so the mainstream agrees with Sanford." The same review, one page after the passage Sanford quotes on neutrality, gives the shares behind "rare": 0% to 15% in five mutagenesis studies.² Both sides say "rare"; they differ by a factor of tens of thousands on what it means.

Issues and unanswered questions

1. The zone below about 2 × 10⁻⁴ is not resolved by the studies reviewed here. None of them sorts individual mutations there, and both sides fill it with a model (Part 7).
2. None of the studies reviewed here gives a direct beneficial share for a multicellular organism in its natural setting. The direct counts here are from microbes and viruses in laboratories, the animal and plant figures come from lines and model fits, and in Johri's human analysis a rare weak beneficial class could not be identified.¹¹
3. Mechanism is not tallied. No study in this article records, for an unselected sample of new beneficial mutations, how many broke a gene and how many tuned or built one.
4. Sources read only in part. For Perfeito 2007, Robert 2018, Lind 2010, Davies 1999, Shaw 2002 and Vassilieva 2000 only the abstract was read. Rozen 2002 and Kassen and Bataillon 2006 were read through later papers' summaries. Kim 2017's supplement, Huber 2017's supplementary tables and Zhen 2021's Table S6 were not reached, so Zhen's 1.5% is read from a figure. Stiffler 2015's class shares are in a full text that could not be downloaded.
5. The "almost 2 per cent" attributed to Wloch 2001. Joseph and Hall 2004 and Sniegowski and Gerrish 2010 credit Wloch's yeast study with a beneficial share near 2%. The Wloch paper read here reports no spontaneous beneficial mutation and two faster-growing induced mutants that it excluded.¹⁹ Wloch's screen was built to find harmful mutations, so it could not supply an unbiased beneficial share in any case. Where the 2% comes from is unresolved.
6. Gerrish's reanalysis has no published number in the text read. Sniegowski and Gerrish 2010 say the 1998 data allow "a much higher estimate" but the passage read gives no value.
7. Dominance. The yeast diploid figures are heterozygous effects. How many of their beneficial mutations would be harmful as homozygotes is unknown; Hall and colleagues name overdominance as one explanation.³³
8. Lethal shares in large genomes. The 20% to 41% lethal shares are for compact genomes. This article does not estimate the lethal share of new mutations in the human genome, which depends on how much of the genome is functional.
9. Two beneficial classes are provisional. The yeast transfer-RNA scan's 1% beneficial rests on a nominal test with no correction for 207 comparisons, under which about three false beneficial calls would be expected by chance if the non-significant mutants were neutral, against about two made; a corrected test or a replicate would settle it.²³ Visher's seven "weakly beneficial" influenza mutants are a growth band, not significance calls, and one viable mutant, HA-8, has no fitness value at all.¹⁵
10. Agreement with the young-earth side on direction does not test the young-earth age. A predominance of harmful mutations among those with an effect is also the standard expectation of population genetics for organisms near an adaptive optimum, so it cannot by itself tell the two histories apart.

Verdict

In the studies reviewed here, measured new mutations with a detectable effect are mostly harmful, and a substantial minority of random changes in compact virus genomes are lethal.  That is also what standard evolutionary genetics expects, so it does not by itself favour a young earth.  Beneficial mutations are rare in the plain sense, but how rare depends on organism, design and conditions:  0 to about 6% of mutants with an effect in the significance-tested virus sets, a fitted 5.75% to 13% in yeast mutation-accumulation lines, more in some algal fits and gene scans, and about 10⁻⁵ per genome per generation in E. coli and yeast experiments designed to see small benefits.

John Sanford's "one million to one" is right about the direction and, as a general rule, wrong by roughly four to five orders of magnitude against those virus sets and small-benefit rate estimates.  Its one real source, Gerrish and Lenski 1998, does say one in a million of all mutations.  It got that figure by solving a model from three sweeps in one E. coli population, under assumptions the authors flagged and the first author later said had held the estimate low.  His other source is about an instrument's power, and a later paper attaches the ratio to the wrong reference.  Michael Behe's different claim, that beneficial mutations are frequent but mostly damaging, is supported on frequency, and the fitness data reviewed here do not test it on mechanism.

Below about 0.02%, none of the methods reviewed here resolves a single mutation's effect.  Neither "almost all harmful" nor "neutral or balanced" is a measurement there, and the evidence in this article does not settle what happens in that zone.

Sources